# Factor Models

> Factor models explain asset returns with common drivers such as the market, size, value and momentum. Learn CAPM, Fama French and how to run a factor regression.

Source: https://learn.tradelabsai.com/portfolio/factor-models/  
Track: Portfolio and Performance · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Factor Models", https://learn.tradelabsai.com/portfolio/factor-models/

A factor model explains the returns of stocks, funds or strategies with a small number of common drivers, called factors. Instead of treating each of thousands of stocks as unique, it says most of their movement comes from shared influences: the overall market, company size, valuation, momentum, industry, interest rates and so on. Factor models are used to measure true alpha, understand where risk comes from, build portfolios and hedge unwanted exposures. They sit at the heart of modern quantitative investing and risk management.

## The general form

```
Excess return = Alpha + Beta1 × Factor1 + Beta2 × Factor2 + ... + Error
```

- **Betas (factor loadings):** how sensitive the asset is to each factor.
- **Factors:** the returns of the common drivers.
- **Alpha:** the return left unexplained.
- **Error:** the asset specific part, which diversifies away in large portfolios.

## Well known factor models

| Model | Factors | Year |
|---|---|---|
| CAPM | Market | 1960s. See [Alpha and Beta](https://learn.tradelabsai.com/portfolio/alpha-and-beta/) |
| Fama French three factor | Market, size (SMB), value (HML) | 1993 |
| Carhart four factor | Adds momentum | 1997. See [Momentum Factor](https://learn.tradelabsai.com/research/momentum-factor/) |
| Fama French five factor | Market, size, value, profitability (RMW), investment (CMA) | 2015 |
| Commercial risk models | Dozens of style, industry and country factors | Used by institutions |

SMB stands for small minus big and HML for high minus low book to market. Factor return data for these models is published free on Kenneth French's website at Dartmouth. See [Size Factor](https://learn.tradelabsai.com/research/size-factor/) and [Value Factor](https://learn.tradelabsai.com/research/value-factor/).

## Types of factor models

| Type | Factors come from | Example |
|---|---|---|
| Macroeconomic | Economic series | GDP growth, inflation, interest rate changes |
| Fundamental | Company characteristics | Size, value, quality, momentum |
| Statistical | Patterns in returns themselves | Principal component analysis |

## Running a factor regression

**Example: Is this fund's alpha real?**
A fund earned an average excess return of 8% a year. A Fama French three factor regression shows a market beta of 1.0, an SMB loading of 0.4 and an HML loading of 0.5. Over the same period the market excess return was 6%, SMB 2% and HML 3%. The factors explain 1.0 times 6% plus 0.4 times 2% plus 0.5 times 3%, which is 6% plus 0.8% plus 1.5%, or 8.3%. The fund's alpha is 8% minus 8.3%, about minus 0.3%. Its outperformance over the market came entirely from tilting toward small and value stocks, exposures that low cost factor funds offer. See [Regression Analysis](https://learn.tradelabsai.com/math/regression-analysis/).

## Uses of factor models

| Use | How |
|---|---|
| Measuring alpha | Separate skill from factor exposure |
| Risk decomposition | See how much risk comes from each factor. See [Risk Contribution and Risk Decomposition](https://learn.tradelabsai.com/portfolio/risk-contribution/) |
| Portfolio construction | Target or neutralise specific exposures. See [Portfolio Construction](https://learn.tradelabsai.com/portfolio/portfolio-construction/) |
| Hedging | Remove unwanted market or sector exposure. See [Hedging](https://learn.tradelabsai.com/markets/hedging/) |
| Performance attribution | Explain past returns by source. See [P&L and Performance Attribution](https://learn.tradelabsai.com/industry/performance-attribution/) |
| Covariance estimation | Estimate correlations of thousands of stocks from a few factors |

## Factor covariance matrices

Estimating correlations directly between 3,000 stocks requires about 4.5 million pairwise values, far more than the data can support reliably. A factor model with, say, 20 factors only needs the factor covariances, each stock's loadings and its specific risk. This produces more stable risk estimates. See [Covariance and Correlation](https://learn.tradelabsai.com/math/covariance-and-correlation/).

## Limitations

- **Factor zoo:** hundreds of published factors, many likely due to data mining. See [P-Hacking and Multiple Testing](https://learn.tradelabsai.com/research/p-hacking-and-multiple-testing/).
- **Unstable loadings:** exposures drift over time.
- **Crowding:** popular factors can suffer sharp drawdowns. See [Factor Timing, Crowding and Crashes](https://learn.tradelabsai.com/research/factor-crowding/).
- **Model choice:** alpha depends on which factors are included.

## Frequently asked questions

### What is a factor model?

A model that explains asset returns using a few common drivers, such as the market, size, value and momentum, plus an asset specific remainder.

### What is the Fama French three factor model?

A model explaining stock returns with the market, a size factor (small minus big) and a value factor (high minus low book to market).

### Why do factor models matter for investors?

They show whether returns come from skill or from known exposures that can be obtained cheaply, and they help measure and control risk.

Next, learn how to keep a portfolio on target in [Rebalancing](https://learn.tradelabsai.com/portfolio/rebalancing/).

## Continue learning

- Next lesson: [Rebalancing](https://learn.tradelabsai.com/portfolio/rebalancing/)
- Previous lesson: [Black-Litterman Model](https://learn.tradelabsai.com/portfolio/black-litterman-model/)
- Related: [Black-Litterman Model](https://learn.tradelabsai.com/portfolio/black-litterman-model/): The Black Litterman model starts from market implied returns and blends in an investor's views with stated confidence, producing stable and intuitive portfolios.
- Related: [Factor Investing Explained](https://learn.tradelabsai.com/research/factor-investing-explained/): Factor investing targets traits linked to long run returns, such as value, momentum and quality. Learn the main factors, the evidence and how they are traded.
- Related: [Alpha and Beta](https://learn.tradelabsai.com/portfolio/alpha-and-beta/): Beta measures how much a portfolio moves with the market; alpha is the return beyond what that exposure explains. Learn formulas, CAPM, regression and pitfalls.
- Related: [Regression Analysis](https://learn.tradelabsai.com/math/regression-analysis/): Regression models how one variable relates to others. Learn linear regression, beta, R squared, multiple regression for factors, hedge ratios and common pitfalls.
- Related: [P&L and Performance Attribution](https://learn.tradelabsai.com/industry/performance-attribution/): Performance attribution explains where returns came from: allocation, selection, factors, Greeks and costs. Learn Brinson attribution, P&L explain and how to use it.
- Related: [Risk Contribution and Risk Decomposition](https://learn.tradelabsai.com/portfolio/risk-contribution/): Risk contribution shows how much each position adds to total portfolio risk, including correlations. Learn marginal and total contributions with a worked example.